Letter pubs.acs.org/macroletters
Confinement Effects with Molten Thin Cyclic Polystyrene Films Qiming He,† Suresh Narayanan,‡ David T. Wu,§ and Mark D. Foster*,† †
Department of Polymer Science, The University of Akron, Akron, Ohio 44325, United States X-ray Science Division, Argonne National Laboratory, Argonne, Illinois 60439, United States § Chemical Engineering and Chemistry Departments, Colorado School of Mines, Golden, Colorado 80401, United States ‡
ABSTRACT: The surface fluctuations of a melt film of a low molecular weight cyclic polystyrene (CPS) manifest confinement effects for a film thickness (14Rg) much larger than that for which a melt film of the linear chain analog manifests confinement. This is true both in terms of absolute thickness and thickness relative to chain size, Rg. In fact, the linear analog polymer does not manifest confinement effects even at a thickness of 7Rg. Both types of films have a strongly adsorbed layer at the substrate that plays a role in slowing the surface fluctuations for the thinnest films. This layer is 70% thicker for the cyclic chains than for the linear chains. At the interface with the substrate the packing of the cyclic chains is perturbed much more strongly than is the packing of the linear chains. hermally stimulated fluctuations on the surfaces of polymer melts dictate key properties including wetting, adhesion,1 and tribology. While these fluctuations are a surface phenomenon, their behavior depends on the mobility of polymeric material deeper in the film as well as at the surface. For a sufficiently thick melt of linear chains the surface fluctuations are overdamped capillary waves.2 At temperatures sufficiently above Tg,bulk, the surface fluctuations that can currently be probed by X-ray specular and off-specular scattering3−7 and X-ray photon correlation spectroscopy (XPCS)2,8−18 are well described by a hydrodynamic continuum theory (HCT).19 This theory yields the surface relaxation time, τ, of a film exhibiting hydrodynamic flow of a continuum characterized by a bulk viscosity, η, and surface tension, γ. The HCT does not take chain molecular architecture into account.19 This theory predicts a universal form for the normalized relaxation time, τ/h, as a function of dimensionless scattering vector, q∥h, where h is the film thickness. For sufficiently thin liquid films, confinement effects can lead to surface fluctuations behaving startlingly different from those of thick films. Supported liquid films of hexane cease to have surface fluctuations in the measurement window of XPCS already for a thickness of 600 Å.20 The apparent viscosities of liquid films of 6−7 molecular layers thick sheared in the Surface Forces Apparatus (SFA) can be orders of magnitude larger than the bulk viscosity due to soft solidity.21 However, confinement effects on surface fluctuations of polymer melts have as yet received limited attention. Confinement effects on surface fluctuations were first reported for films of 90k linear polystyrene (LPS) by Wang et al.6 on the basis of static scattering data. Those authors looked in diffuse scattering data for the signature of suppression of capillary waves for sufficiently large wavelengths and found a lower cutoff value of scattering vector that increased as film thickness decreased. The suppression of the surface fluctuations was attributed to van der Waals interactions between the melt surface and
T
© 2016 American Chemical Society
underlying substrate. Sinha and collaborators9 subsequently reported that for substantially entangled LPS chains (123k) the universal behavior anticipated by the HCT was lost with decreasing film thickness when the thickness dropped to about 4Rg (376 Å). The dependence of τ on q∥ changed and this dependence could only be described by adding a modulus to the model for the continuum to describe viscoelasticity. For a film of thickness equal to Rg (94 Å) no fluctuations were seen. For these melts of entangled linear chains, the confinement effect was attributed to the pinning of chains to the substrate by physisorption of some segments.22−26 Foster and co-workers12 have shown, however, that even with a melt of a low molecular weight polystyrene having cyclic architecture (CPS) and, therefore, no entanglements, for sufficiently low thickness, the fluctuations are slower than anticipated from the HCT. In contrast to the data of Jiang et al.9 for entangled linear chains, the shape of the τ versus q∥ curves for the low molecular weight cyclic chains does not change with decreasing thickness over the thicknesses probed, which suggests an effective film viscosity higher than the bulk value. For a 14k CPS, this can be seen at a thickness between 220 Å (∼10Rg) and 440 Å (∼20Rg). Data on the thicknesses for which confinement can be seen for other chain architectures are sparse, but sufficient to hint that these effects become important for some architectures at larger thicknesses than for other architectures. Notably, for star-like architectures it appears there may be deviations from the HCT behavior for films with thicknesses of order 20Rg.12 In this Letter we show that, although the cyclic chains have smaller Rg than do their linear analogs, they show confinement effects at larger film thicknesses. For 6k cyclic chains confinement appears at 241 Å (∼14Rg), while for linear analogs, no confinement is apparent Received: June 29, 2016 Accepted: August 4, 2016 Published: August 8, 2016 999
DOI: 10.1021/acsmacrolett.6b00497 ACS Macro Lett. 2016, 5, 999−1003
Letter
ACS Macro Letters
nonslip boundary condition holds at the film−substrate interface, the thickness normalized relaxation time is given as a function of q∥h as
even at 154 Å (∼7Rg). This difference is due to the fact that the strongly adsorbed sublayer at the substrate is much thicker for the cyclic melt than for the linear melt. Pure melt films of LPS (Mn = 6000 ± 600 g/mol; PDI = 1.02; Tg,bulk = 87.0 °C by differential scanning calorimetry; synthesized by anionic polymerization using sec-butyl lithium as initiator and terminated by methanol) and CPS (Mn = 6000 ± 600 g/mol; PDI = 1.03; Tg,bulk = 98.9 °C; synthesized by a combination of anionic polymerization and metathesis ringclosure27) were spun cast onto polished silicon wafers from toluene (EMD, 99.5%) solutions of concentrations appropriate to achieve target film thicknesses. Wafers were cleaned with piranha solution,28 and the native oxide layer removed using a 1% aqueous solution of hydrofluoric acid (Aelf Aesar, ACS). The solution for spin-casting was placed on the substrate about 20 s after finishing the etching and no SiOx layer had to be included in models of the samples to fit X-ray reflectivity curves well. The films were annealed in high vacuum (ca. 1 × 10−7 Pa) at 120 °C for 12 h before the XPCS measurements. The nominal film thicknesses measured with reflectivity at 140 °C were 148, 181, 241, 286, 411, 645, and 1211 Å for CPS and 154, 340, and 752 Å for LPS, respectively, with uncertainties of fitting thickness of ±1 Å. For a given temperature the variation in thickness over the footprint of the beam was generally < ± 10 Å. Measurements were carried out at beamline 8-IDI at the Advanced Photon Source using a partially coherent X-ray beam (7.35 keV, 20 × 20 μm) with coherence lengths of 7 and 140 μm in the horizontal and vertical directions, respectively. The instrument geometry and analysis procedure have been described elsewhere.2,12 The incident angle, θi, of 0.14° was below the critical angle of PS (0.16°). The speckle pattern was recorded using a two-dimensional CCD camera after equilibrating a sample for 20 min at a given temperature. Relaxation times for the surface fluctuations were derived from fitting intensity−intensity autocorrelation functions calculated from the data. The data were checked for the influence of beam damage by comparing correlation results obtained using various subsets of all the frames available and suspicious frames discarded. After the XPCS measurements, a CPS film and an LPS film were rinsed by placing each in a toluene bath and the bath covered for 10 min. After that, the film was dried with a stream of nitrogen for 30 s to displace chains not strongly adsorbed.26 The dipping and drying steps were repeated four times (for a total of five rinses). After that, the film was annealed in high vacuum (ca. 1 × 10−7 Pa) overnight at 25 °C before performing X-ray reflectometry (XR) measurements. An XR measurement of the residual layer with a parallel beam optic spectrometer on a rotating anode source (12 kW, λ = 1.54 Å) revealed the thickness, density, and roughness of the residual layer tenaciously adsorbed to the substrate.22−26 The intensity−intensity autocorrelation function, g2, from the XPCS measurement is given by
2η[cosh2(q h) + (q h)2 ] τ = h γq h[cosh(q h)sinh(q h) − q h]
Surface tension values for the CPS and LPS used for the data analysis are listed in Table 1. Those for the linear analog were Table 1. Surface Tensions of 6k Macrocyclic Polystyrene and Its Linear Analog
a
⟨I(q , t ′)⟩2
temp (°C)
γlineara (mN/m)
110 120 130 140 150 160
33.4 32.8 32.2 31.5
γcyclica (mN/m)
32.3 31.6 31.0
The uncertainty of the surface tension is about ±5%.
interpolated from literature data,29 while those for the cyclic analog30 were derived from those for the linear chains by accounting for the lack of end groups using a calculation introduced by Koberstein.31 The effects on relaxation times of central interest here are sufficiently large that the uncertainties in the melt surface tensions are not critical to the conclusions. The film viscosity, ηXPCS, can be inferred by fitting the data of τ/h versus q∥h when the assumptions of the HCT are valid. Normalized relaxation times for our linear analog, shown in Figure 1, provide a base case against which those for the chains
Figure 1. τ/h vs q∥h for LPS films at various temperatures. The dashed curves represent least-squares fits to the HCT with ηXPCS as a fitting parameter.
⟨I(q , t ′)I(q , t ′ + t )⟩ g2(q , t ′) =
(2)
(1)
of nonlinear architecture may be compared. Data from three linear chain films of thicknesses 154, 340, and 752 Å collapse onto a universal curve for each temperature, and no confinement effect is observed. The corresponding data and fits for the CPS films, shown in Figure 2, show confinement effects for thicknesses less than about 286 Å at 140 °C (T − Tg = 41 °C). Data from films of thickness 241 Å or less do not collapse onto the universal
where I(q∥, t′) is the scattering intensity at q∥ at time t′, and the angular brackets refer to ensemble averages for the delay time t. For the overdamped capillary waves, a single exponential decay, g2 = 1 + β exp(−2t/τ) with speckle contrast β and relaxation time τ,2 provided a good fit of the g2 function shape. According to the HCT, the relaxation time depends on η, γ, the thickness of the film, h, and the in-plane wave vector, q∥.2,19 When a 1000
DOI: 10.1021/acsmacrolett.6b00497 ACS Macro Lett. 2016, 5, 999−1003
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ACS Macro Letters
Figure 3. Comparison of viscosities obtained from XPCS data (open symbols) with viscosities from bulk rheology (filled symbols) as a function of temperature for LPS and CPS.
about 7Rg. We note that relative to the size of the linear chain involved, this thickness still exceeds the limit of 4Rg found by Jiang et al.9 for confinement effects in films of large, entangled linear chains. It is conjectured that in this case physisorption of chain segments to the substrate could create a kind of Guiselin brush,32 restricting chain motion and resulting in an elastic component to the films viscoelastic behavior. Here our molecular weight is too small for entanglement effects to play a role, allowing us to probe a different regime of behavior. The viscosities from the XPCS universal curves for the cyclic chain are within 30% of the values extrapolated from the literature bulk rheology data at 150 and 160 °C.30 For 140 °C, the agreement is good, and still within the factor of 2 agreement seen by Kim et al.2 for linear chains. The key observation is that, for the films of cyclic chains, the confinement effects begin to manifest themselves at a thickness, hc,cyclic, of 241 Å (14Rg), while for the linear chains, no confinement effects are observed even for a lower thickness of 154 Å (7Rg) at comparable values of T − Tg. Both the absolute and the relative film thicknesses at which the confinement effects are seen for the cyclic chains are consistent with the much less well-resolved result for 14k CPS for which Wang et al.12 saw confinement appear between thicknesses of 440 Å (20Rg) and 220 Å (10Rg) for T − Tg of 32 °C. Although the τ/h data for the CPS films thinner than 241 Å lie above the HCT model curve, the slopes of the curves (Figure 2) for these smaller thicknesses are similar to those of the universal curve. That is, there is no evidence of a qualitative change in the character of the film dynamics underlying the surface fluctuations as there was for entangled, longer linear chain films.9 The data for the CPS films of small thicknesses can be fitted with the HCT just using an effective viscosity higher than the bulk value or a smaller effective thickness of the mobile film, without having to include a shear modulus. To investigate the basis for the difference in confinement effects in the CPS and LPS films, the strongly adsorbed “residual” layer at the substrate interface was probed using XR. The CPS residual layer was 34 Å, or about 2Rg thick, while the LPS residual layer was 20 Å, or about 1Rg, thick, based on estimates of the Rgs extrapolated from literature values.33 This difference in the thickness of the immobile layer at the substrate is reason enough to expect a difference between hc,cyclic and hc,linear. It is not sufficient, however, to formulate a full explanation of the magnitude of the difference. The manner in which neighboring cyclic chains interact with their immobile
Figure 2. τ/h vs q∥h for CPS films with various thicknesses at (a) 140 and (b) 150 and 160 °C. Dashed curves represent a least-squares fit to the HCT using the data for h > 243 Å.
behavior. For 150 and 160 °C the trend of increasing deviation from the universal curve with smaller thickness is even stronger. Values of the viscosities derived from the HCT fits are compared with those from bulk rheology measurement results in the literature,29,30 ηbulk, in Figure 3. For the 6k linear chains the agreement is within 10% at 110 and 120 °C. At 130 and 140 °C the values from XPCS are approximately a factor of 2 below the bulk values,29 which is still within the range of agreement between ηXPCS and ηbulk seen by Kim et al.2 for linear chains. The HCT theory using a nonslip condition captures the features of the surface fluctuations of LPS samples when the thickness of the film is larger than 151 Å, which corresponds to 1001
DOI: 10.1021/acsmacrolett.6b00497 ACS Macro Lett. 2016, 5, 999−1003
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imentally from the fact that for a blend film of 2k linear and cyclic PS chains,34 the linear chains enrich the surface. This can be predicted with a Wall-PRISM theory that accounts for local packing differences.34 It is also known that the bulk viscosities of low molecular weight cyclics are higher than those of their linear analogs,12,29 so certainly cyclic polystyrenes exhibit more efficient packing in the bulk as compared to their linear counterparts. Recent simulations38 show that small cyclic chains pack more densely at a hard wall than do their linear analogs and thus our results are consistent with the simulations. Here a difference in packing is strikingly demonstrated by a much larger thickness for the residual layer in the case of the cyclic chains. We argue that, while differences in mobility at the air interface could also play a role, this packing difference at the substrate is a major reason for the confinement effects manifesting themselves at larger relative thicknesses for cyclic chains than for linear chains.
layer is most probably different from that with which neighboring linear chains interact with their immobile layer. Based on recent results of Torkelson and co-workers34 on variation of Tg with film thickness for linear and cyclic chains, we may argue that in the film of linear chains there is a mobile layer35,36 at the surface, while for the film of cyclic chains, any increase in mobility at the surface is not as large.34,37 When the CPS surface fluctuation data are plotted using as effective film thicknesses defined as the original film thickness minus the residual layer thickness, the data collapse reasonably well onto an universal curve at 140 °C as shown in Figure 4, in agreement
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AUTHOR INFORMATION
Corresponding Author
*E-mail:
[email protected]. Notes
The authors declare no competing financial interest.
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ACKNOWLEDGMENTS We thank Caleb Tomey for assistance with the analysis of the immobile layer thickness and The University of Akron Research Foundation for funding.
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Figure 4. Collapse of the τ/h vs q∥h data at 140 °C achieved by analyzing the data using a two-layer model for CPS films shown in the inset.
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